Abstract
Precision measurements of the Lu$^+$ $^3D_1$ and $^3D_2$ quadrupole moments have been carried out giving $\Theta(^3D_1)=0.63862(74)\,e a_0^2$ and $\Theta(^3D_2)=0.8602(14)\,e a_0^2$, respectively. The measurements utilize the differential shift between ions in a multi-ion crystal so that effects of external field gradients do not contribute leaving only the well defined Coulomb interaction. At this level of precision, hyperfine-mediated corrections will likely be important.
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